Part 7. Electric conductivity of solutions
1
PART 7
ELECTRIC CONDUCTIVITY OF
SOLUTIONS
I. MOTION OF IONS IN ELECTRIC FIELD.
The electric current in solutions is transferred by ions and not by
electrons as it is in metals.
For this reason the ionic motion in electric field has to be discussed prior
to the discussion of electric conductivity.
When a solution is subjected to electric field, cations (positive ions) start
to move towards cathode (negative electrode) and anions (negative ions)
start to move towards anode (positive electrode). Motion of an ion in the
electric field is a broken line, as lots of collisions with other ions and
solvent molecules occur, when the ion is moving.
The real way of ion therefore is not known, but the projection of its
motion on the direction of electric field is used for calculation of the speed
of ion's motion. As usually, speed of ion, v, is calculated as the distance,
covered by ion, divided by time:
v
l
t
2
A.Rauhvargers. GENERAL CHEMISTRY
The speed of ion itself is not a characteristic value for the ion, because
the speed depends on the intensity of electric field, too. Another value,
called mobility of ion is used, when it is necessary to compare the motion of
different ions in electric field.
Mobility of ion is defined as the speed of ion, divided by intensity
of electrical field, E (volts/cm):
V
U
E
where
U is mobility of ion.
Usually U+ is used as a symbol for mobility of a positive ion and U- is
used as a symbol for mobility of a negative ion.
l
Fig.7.1. Motion of ion in electrical field
I.2. FACTORS, AFFECTING THE MOBILITY OF ION
The mobility of ion is affected by the following factors:
1) viscosity of solution, the greater it is, the smaller will be the mobility
of ion,
2) hydration of ion - the greater is hydration, the smaller becomes
mobility, because the ion has to carry molecules of water with it when
it is moving. There are 3 more factors, that affect mobility of ion
through their action to hydration:
a) sign of ion's charge - a cation is always less hydrated, than an
anion of the same size. This phenomenon can be explained as
follows. Ions are hydrated, because their charge electrically
Part 7. Electric conductivity of solutions
3
attracts the partly charged ends of water molecules. In the case of
anion, the negative charge of ion is carried by electrons, that are
situated close to the outer surface of the ion, therefore the
effective charge on the surface of ion is rather great and many
water molecules are attracted. A cation, having the same size, is
positively charged. The positive charge is located on the nucleus,
which is, as we know, placed in the middle of ion. For this reason
the effective charge on the surface of ion is lower, then in case of
anion, having same absolute value of charge and same size, and,
hence, cation attracts smaller number of water molecules.
b) the second factor, acting on the mobility through hydration, is the
size of ion - the greater is the size of ion, the smaller is its
hydration, because the force of electric attraction is determined by
Coulomb's law:
q q
F  12 2 ,
r
where
F is the force of electric attraction,
q1 and q2 are the charges of the two particles,
r is the distance between the two particles.
From this formula one can see, that, the greater is size of ion
(radius r), the smaller is the force, that attracts a water molecule
and, hence, small ions are more hydrated, than big ones.
c) the third factor, acting through hydration is charge of ion. The
greater is the charge of ion, the more hydrated it is and, hence, the
smaller is its mobility. (Here one could say, that, the greater is the
charge of ion, the more it is attracted by the appropriate pole of
electric field, but the effect of charge on hydration here is more
impressive and for this reason univalent ions, like K+, Na+, Clare more mobile, than polyvalent, as Ca2+, Al2+, SO42- etc.)
3) Next factor, affecting the mobility of ion is temperature. Action of
temperature is complex - on one hand, a raise of temperature increases
the thermal motion of water molecules and more collisions occur on
the ion's way to the appropriate pole, thus decreasing the mobility of
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A.Rauhvargers. GENERAL CHEMISTRY
the ion, on the other hand, the raise of temperature decreases the
viscosity of solution and the hydration of ions and, thus, increases the
mobility of ion. Finally the effect of temperature on hydration and
viscosity is greater, than its effect ion the number of collisions and the
mobilities of ions increase for about 2%, when t° is raised for 1
Kelvin.
4) the mobility of ion is affected by the concentration of solution - the
greater is concentration, the more collisions with ions of opposite sign,
that move in the opposite direction, happen on the ion's way, and the
mobility grows smaller. Mobility increases at dilution of solution and
at high enough dilution (a low enough concentration) reaches a
constant value, U called mobility at infinite dilution. Values of U
for most of ions are measured and given in the chemical tables.
I.3.ANOMALOUS MOBILITIES OF H+ AND OH- IONS.
These two ions have abnormally great mobilities, that are 8-10 times
greater than the mobilities of all other ions. This could seem a strange
phenomenon, especially for H+, because H+ is very small and, thus, has a
great hydration. The explanation of this phenomenon is, that H+ and OHions have a special mechanism of transfer in water solutions. In contrary to
all other ions, the motion of H+ and OH- ions in the electric field is not a
broken line, discussed before. As it will be shown, the motion of H+ and
OH- ions in electric field is very similar, because the motion of OH- ions
can finally be reduced to motion of H+ ions in the opposite direction. An
H+ ion in the solution exists as a H2O and its motion towards the negative
pole in fact consists of repeated transfers of the proton H+ from one water
molecule to another one, then to next one, etc.:
Part 7. Electric conductivity of solutions
step 1
+
step 2
step 3
H+
5
H2O H2O H2O
+
H
+
H 3O H2O H2O
+
H
+
H2O H 3O H2O
-
The motion of an OH- ion in the electric field is carried out as repeated
transfers of H+ ion in the opposite direction, resulting as a motion of OHH
step 1
+
H2O H2O H2O
H
step 2
step 3
H2O
OH -
+
H2O H2O OH
H
+
+
-
OH - H2O
As a result of all this, the motion of H+ and OH- in electric field is a
straight line (compare to the situation in fig.7.1) and therefore the mobilities
of these two ions are great. This property of H+ and OH- ions is used in
conductometric titration (see further).
II. EQUIVALENT CONDUCTIVITY
Equivalent conductivity of an electrolyte is the conductivity, observed,
when 1 equivalent of electrolyte (in dissolved state) is situated between two
electrodes, that are located in a distance of 1 cm from each other, see
fig.7.2.
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A.Rauhvargers. GENERAL CHEMISTRY
1 equivalent
V cm3
1 cm3
Fig.7.2. Illustration of equivalent conductivity
As a whole equivalent of electrolyte is situated between the electrodes,
the equivalent conductivity is increasing by dilution (decrease of
concentration), because for an equal amount of electrolyte (1 equivalent) it
is much easier to transfer current, if the solution is more diluted. The
concentration dependence of the equivalent conductivity () is different for
strong and weak electrolytes, see fig.7.3.
Fig.7.3. Dependence of equivalent conductivity on solution
concentration for strong and weak electrolytes.
In general, the equivalent conductivity depends on the dissociation
degree of electrolyte and on the mobilities of ions. For a strong electrolyte,
as KCl, the dissociation degree (the real ) is equal to  at any
Part 7. Electric conductivity of solutions
7
concentration. The slight increase of  at a decrease of concentration occurs
due to the increase of ionic mobilities. For a weak electrolyte, as
CH3COOH, at great concentrations  is very low, therefore  is low, too.
The slight increase of  with the decrease of concentration occurs both
due to the growth of mobilities and due to the growth of .
As dissociation degree is increasing by dilution of solution

K
C
at very low concentrations  starts to grow rapidly, as the dissociation
degree of all the weak electrolytes at infinite dilution reaches the value
1 , too. Any electrolyte at infinite dilution reaches a characteristic for it
value of equivalent conductivity, called the equivalent conductivity at
infinite dilution . This is related to the ionic mobilities at infinite
dilution:


   F(U   U  ) (Kohlrausch's law)
where
F is Faraday's number.


U  and U  are cation and anion mobilities at infinite
dilution
As the ionic mobilities at infinite dilution can be found in the chemical
tables,  an easily be calculated.
III. DETERMINATION OF THE DISSOCIATION
DEGREE BY MEANS OF CONDUCTIVITY
MEASUREMENTS.
Equivalent conductivity, , at a given concentration depends on the
dissociation degree of the electrolyte, or, more precisely, it is proportional
to the dissociation degree:
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A.Rauhvargers. GENERAL CHEMISTRY
 = b,
where b is a proportionality coefficient.
At infinite dilution,
= I but  = 
From here one can easily see, that the proportionality coefficient b is in
fact equal to :
= 
If the equivalent conductivity of an electrolyte is measured and the
equivalent conductivity of the same compound at infinite dilution is
calculated from Kohlrausch's law, dissociation degree is found as:



For a strong electrolyte the value of , thus obtained, is the imaginary ,
as the real dissociation degree of a strong electrolyte is 1.
When  of the weak electrolyte is determined, one can calculate its
dissociation constant, using Ostwald's dilution law:
 2C
K
1
Measurements of the electric conductivity is one of the most common
methods for determination of dissociation constants.
IV.CONDUCTOMETRIC TITRATION
Conductometric titration is a method of titration, in which the endpoint is
indicated, using a rapid change of the conductivity of solution. As well as
potentiometric titration, it is used in the cases, if the solution is dark or
turbid and the use of color indicators becomes impossible, or there is no
color indicator for the reaction, that is used at titration.
Part 7. Electric conductivity of solutions
9
The main application of conductometric titration is its use for acid - base
titration. One important advantage of this method is, that a mixture of
strong and weak base can be titrated and two separate endpoints - one for
strong and one for weak acid (or base) can be found, and consequently,
concentrations of strong and weak acid can be determined separately (in
fact, this can also be done, using potentiometric titration).
Conductometric acid-base titration uses the abnormally high mobilities of
H+ and OH- ions. Practically this titration is carried out in such a way, that
two similar electrodes (usually platinum or graphite) are immersed into the
solution and the resistance of solution is measured. Value of reciprocal
resistance I/R is used instead of real conductivity because I/R is
proportional to conductivity and it is easier to measure the resistance of a
solution,
Conductometric titration curves will be discussed for titrations of strong
acid, weak acid and a mixture of strong and weak acid by a strong base
(NaOH).
IV.I. TITRATION OF STRONG ACID (HCl)
When HCl is titrated by NaOH, the reaction is
H+ +Cl- + Na+ + OH -  Na+ + Cl- + H2O
Equation is written in ionic form in order to have a possibility to judge
about the electric conductivity of solution. Here and further in the reaction
equations the titrant is "wrapped" to show, that, as soon as it is added, it
reacts and therefore it should not be taken into account, when considering
the conductivity before the titration endpoint.
As one can see, Cl- ions appear in both sides of equation, therefore they
don't change the conductivity of solution. The result of the reaction of HCl
with NaOH, from conductivity point of view is, that H+ ions, that are
extremely mobile, are changed to Na+ ions, that have a "normal" mobility.
While there is HCl in the solution, all the added NaOH is immediately used
in the reaction with HCl (and, therefore there can be no NaOH in the
solution yet).
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A.Rauhvargers. GENERAL CHEMISTRY
Thus, before the endpoint of titration, the addition of NaOH solution
causes a decrease of conductivity - the more H+ ions are replaced by Na+
ions, the lower becomes the conductivity of solution, see fig.7.4.
1/R
VNaOH
Vendpoint
Fig.7.4. Conductometric titration curve for titration of a strong acid,
by NaOH.
At the endpoint of titration all the HCl is used up and further addition of
NaOH causes an increase of conductivity due to the appearance of OHions, which, as well as H+ ions have a very great mobility. The titration
endpoint (the volume Vendp. of NaOH in fig.7.4., used for reaction with
HCl) is found from the titration curve as the abscissa of the break point of
the titration curve.
IV.2. TITRATION OF A WEAK ACID (CH3COOH) BY NaOH
When CH3COOH is titrated by NaOH, the reaction equation looks as
follows:
CH3COOH + Na+ + OH -  CH3COO- + Na + + H2O
Acetic acid can be considered as non-dissociated from conductivity point
of view - even at rather little concentrations its association degree is about
1%. CH3COONa as a salt is a strong electrolyte and therefore is
Part 7. Electric conductivity of solutions
11
completely dissociated. As one can see from the reaction equation, the
reaction of acetic acid with NaOH from conductivity point of view is a
change of non-dissociated acid, having no electric conductivity, to a salt,
that has a measurable electric conductivity (NaOH doesn't affect the
conductivity before endpoint, as it is immediately used in the reaction while
acetic acid is still present).
1/R
VNaOH
Vendpoint
Fig.7.5. Conductometric titration curve for titration of a weak acid
by NaOH.
This means, that already before the titration endpoint, conductivity of the
solution must increase - the more NaOH is added, the more non-dissociated
acid is replaced by the salt. Increase of the conductivity before the endpoint
is slow (see in fig.7.5.), because Na+ and CH3COO- ions have small
mobilities.
As soon as the last molecule of acetic acid is used, free NaOH appears in
the solution and conductivity starts to grow quickly, as the concentration of
the extremely mobile OH- ion increases. Actually, the branch of the
titration curve after the endpoint is absolutely identical to the one at
titration of a strong acid. The endpoint of titration (Vendpoint) again is
found as the abscissa of the break point of titration curve.
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A.Rauhvargers. GENERAL CHEMISTRY
IV.3. TITRATION OF A MIXTURE OF STRONG AND WEAK ACID
(HCl + CH3COOH).
In order to understand, why it is possible to detect the endpoints for each
acid separately, one has to compare the dissociation reactions of both acids:
HCl  H+ + ClCH3COOH
H+ + CH3COO-
1/R
VNaOH
V
I
VII
Fig.7.6. Conductometric titration curve for titration of a mixture of
strong and weak acids by NaOH.
HCl as a strong electrolyte is dissociated completely and H+ ions from
the dissociation of HCl oppress the dissociation of acetic acid (as they are
products of the dissociation equilibrium of acetic acid).
For this reason, while HCl is present in solution, acetic acid remains in
molecular form only, and, consequently, all H+ ions, that react with added
OH- ions, come from HCl. Thus, HCl ids used first and the neutralization
of acetic acid begins after all HCl is used.
According to this, the titration curve in fig.7.6 has 3 branches 1) branch of strong acid,
2) branch of weak acid,
Part 7. Electric conductivity of solutions
13
3) branch of NaOH.
The curve has 2 break points (VI and VII) and therefore two separate
volumes of NaOH can be found - one for neutralization of the strong acid
and one for neutralization of the weak acid.
V.ELECTRIC CURRENT IN BIOLOGICAL
OBJECTS
V.1.TRANSFER MECHANISMS OF DIRECT AND ALTERNATING
CURRENT IN TISSUES
When living cells are subjected to outer electric field, different
conductivity mechanisms are observed for direct current and for alternating
current.
When direct electric field is switched on, all the positive ions start
motion towards cathode (negative electrode) and all the negative ions start
motion to anode (positive electrode), therefore a pulse of electric current is
observed at the first moment. This pulse is very short and after it the current
drops to almost zero level - as soon as ions have reached the cell walls, they
are stopped, because the cell walls are not permeable for ions (or, at least,
the permeability is too low to create measurable electric current).
While the outer electric field is on, cations gather at one end of the cell
(the one, that is closer to cathode) and anions gather at the other end of cell
- the cell is polarized.
Mechanism for transfer of alternating current is different. If alternating
electric field is switched on, the ions start to move to the appropriate
electrodes, as well, but the polarity of the outer field changes to the
opposite one while they haven't yet reached the cell walls therefore the ions
start to move in the opposite direction, then polarity changes again and so
on.
If the frequency of alternating field is high enough and ions don't reach
cell walls in a half-period's time, nothing interferes the motion of ions and
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A.Rauhvargers. GENERAL CHEMISTRY
therefore the conductivity for alternating current is high. In other words,
living cell acts as a condenser - it is closed for DC, but open for AC.
It is possible to use the difference in the mechanisms of AC and DC
transfer for judging about the state of cell membranes. If a liquid,
containing living cells has to be investigated, one can measure the
conductivity of solution for AC and for DC. If the cell membranes are
intact, the conductivity, as it was described before, will be high for AC and
low for DC. If the cell membranes are broken, there will be no difference in
the conductivities for AC and DC.
V.2. PHYSIOLOGICAL EFECT OF CATHODE AND ANODE
In some of the physiotherapy procedures, electrodes are placed on a
patient's skin and the electric field is switched on. The physiological effects
of cathode and anode are different.
EFFECT OF CATHODE.
As soon as electric field is switched on, all positive ions start motion to
cathode. The most common positive ions in biological objects are H+, K+,
Na+, Ca2+ and Mg2+.
As the univalent ions are much more mobile, than the polyvalent ones,
therefore they reach cathode zone first and a relative excess of univalent
positive ions is formed under cathode. The presence of K+, Na+ and H+
ions under cathode increase the permeability of the cell wall and it becomes
permeable to substances, for which it is not permeable without electric
field.
For this reason cathode can be used for infusion of medicine into cells the solution of medicine has to be smeared on the skin of patient under the
cathode.
Effect of anode.
As it was already said, the univalent metal ions, that are more mobile,
are quickly shifted towards cathode, if electric field is switched on. As
bivalent metal ions Ca2+ and Mg2+ are less mobile, an excess of Ca2+ and
Mg2+ ions in the anode zone is formed after the univalent ions escape.
Excess of bivalent cations in the anode zone causes a decrease of the
Part 7. Electric conductivity of solutions
15
permeability of cell membranes in this zone. This phenomenon is used to
alleviate pains during the treatment of consequences of traumas and to fight
with inflammations, for instance, after pneumonia. As the cell membranes
are closed in anode zone (their permeability is lowered), cell is "left alone"
and can slowly restore its normal condition.
Besides these direct actions of cathode and anode, pH is changed during
electro therapy - H+ ions move to cathode and OH- ions - to anode circulation processes of biological liquids are intensified, which results in
faster liquidation of inflammation.